Northampton Electronic Collection of Theses and Research

Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical model

Kaczmarczyk, S. and Ostachowicz, W. (2003) Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical model. Journal of Sound and Vibration. 262(2), pp. 219-244. 1095-8568.

Item Type: Article
Abstract: The classical moving co-ordinate frame approach and Hamilton's principle are employed to derive a distributed-parameter mathematical model to investigate the dynamic behaviour of deep mine hoisting cables. This model describes the coupled lateral–longitudinal dynamic response of the cables in terms of non–linear partial differential equations that accommodate the non-stationary nature of the system. Subsequently, the Rayleigh–Ritz procedure is applied to formulate a discrete mathematical model. Consequently, a system of non-linear non-stationary coupled second order ordinary differential equations arises to govern the temporal behaviour of the cable system. This discrete model with quadratic and cubic non-linear terms describes the modal interactions between lateral oscillations of the catenary cable and longitudinal oscillations of the vertical rope. It is shown that the response of the catenary–vertical rope system may feature a number of resonance phenomena, including external, parametric and autoparametric resonances. The parameters of a typical deep mine winder are used to identify the depth locations of the resonance regions during the ascending cycles with various winding velocities
Subjects: T Technology > TJ Mechanical engineering and machinery > TJ1350 Hoisting and conveying machinery
T Technology > TN Mining engineering. Metallurgy
T Technology > TA Engineering (General). Civil engineering (General) > TA349 Mechanics of engineering. Applied mechanics > TA355 Vibration
Creators: Kaczmarczyk, Stefan and Ostachowicz, W
Publisher: Elsevier
Faculties, Divisions and Institutes: University Faculties, Divisions and Research Centres - OLD > School of Applied Sciences (to 2009)
Date: 1 January 2003
Date Type: Publication
Page Range: pp. 219-244
Journal or Publication Title: Journal of Sound and Vibration
Volume: 262
Number: 2
Language: English
ISSN: 1095-8568
Status: Published / Disseminated
Refereed: Yes
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